Linear Algebra - Row Space of a matrix

1 - About

3 - Theorem

3.1 - Echelon

If a matrix is in echelon form, the nonzero rows form a basis for the row space.

3.2 - Row-addition

Applying elementary row-addition operations does not change the row space.

4 - How to

4.1 - find a basis

To find basis for row space of a matrix A, iteratively transform A into a matrix B

  • in echelon form
  • with no zero rows
  • whose row space is the same as that of A.

See Gaussian elimination - Finding a basis for the computation

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